More Puzzles

During the lunch hour at school, a group of five boys from Miss Jones home room visited a nearby lunch wagon. one of the five boys took a candy bar without paying for it. When the boys were questioned by the school principal, they made the following statements in respective order:
1. Rex: "Neither Earl nor I did it."

2. Jack: "It was Rex or Abe."

3. Abe: "Both Rex and Jack are lying."

4. Dan: "Abe's statement is not true; one of them is lying and the other is speaking the truth."

5. Earl: "What Dan said is wrong."

When Miss Jones was consulted, she said, "Three of these boys are always truthful, but everything that two of them say will be a lie." Assuming that Miss Jones is correct, can you determine who took the candy bar?

Since Dan and Earl contradict each other one of them must be lying. If Earl is lying then Abe is lying and so is one of Rex and Jack, which is not possible (Earl + Abe + one of Jack and Rex = 3 liars). If Earl is telling the truth, then Dan is lying. However, only one part of Dan's statement has to be false for him to be lying, if the first part is false then that means that both Jack and Rex are lying, which is impossible again (Dan + Jack & Rex = 3 liars), which means the first part is definitely true and the second part is surely false. This means that not only is the statement (one of [jack and rex] is lying and the other telling the truth) false, but so is (both jack and rex are lying) leaving only one possibility, that they are both telling the truth.

So:
Truth-tellers:
Rex, Jack, Earl
Lairs:
Dan & Abe

So Rex says that neither Earl nor he did it, which we know is true
Jack says it was Rex or Abe, but because what Rex said was true, it cannot be Rex so Abe is the culprit.
=)

[quote="alexonfyre"]Since Dan and Earl contradict each other one of them must be lying. If Earl is lying then Abe is lying and so is one of Rex and Jack, which is not possible (Earl + Abe + one of Jack and Rex = 3 liars). If Earl is telling the truth, then Dan is lying. However, only one part of Dan's statement has to be false for him to be lying, if the first part is false then that means that both Jack and Rex are lying, which is impossible again (Dan + Jack & Rex = 3 liars), which means the first part is definitely true and the second part is surely false. This means that not only is the statement (one of [jack and rex] is lying and the other telling the truth) false, but so is (both jack and rex are lying) leaving only one possibility, that they are both telling the truth.

So:
Truth-tellers:
Rex, Jack, Earl
Lairs:
Dan & Abe

So Rex says that neither Earl nor he did it, which we know is true
Jack says it was Rex or Abe, but because what Rex said was true, it cannot be Rex so Abe is the culprit.
=)